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Time and frequency responses of non-integer order RLC circuits

  • Received: 02 October 2018 Accepted: 26 December 2018 Published: 08 January 2019
  • By introducing an auxiliary parameter, the dynamic of RLC electrical circuits of non-integer order is described by a fractional order differential equation. The order of derivative in the component models is assumed to be zhongwenzy \lt \gamma\leq 1$. The time and frequency domain characteristics of the circuit is investigated, and it is shown that three different filter characteristics of low-pass, high-pass and band-pass filters are obtained. The filter parameters are determined analytically, and the results are verified numerically.

    Citation: Mehmet Emir Koksal. Time and frequency responses of non-integer order RLC circuits[J]. AIMS Mathematics, 2019, 4(1): 64-78. doi: 10.3934/Math.2019.1.64

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  • By introducing an auxiliary parameter, the dynamic of RLC electrical circuits of non-integer order is described by a fractional order differential equation. The order of derivative in the component models is assumed to be zhongwenzy \lt \gamma\leq 1$. The time and frequency domain characteristics of the circuit is investigated, and it is shown that three different filter characteristics of low-pass, high-pass and band-pass filters are obtained. The filter parameters are determined analytically, and the results are verified numerically.


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    [1] R. Metzler, J. Klafter, The restaurant at the end of the random walk: recent developments in the description of anomalous transport by fractional dynamics, J. Phys. A: Math. Gen., 37 (2004), 161-208. doi: 10.1088/0305-4470/37/1/011
    [2] O. Tokatlı , V. Patoglu, Using fractional order elements for haptic rendering, Springer Proceedings in Advanced Robotics, 2 (2018), 373-388. doi: 10.1007/978-3-319-51532-8_23
    [3] A. Karthikeyan, K. Rajagopal, FPGA implementation of fractional-order discrete memristor chaotic system and its commensurate and incommensurate synchronizations, Pramana-J. Phys., 90 (2018), 1-13. doi: 10.1007/s12043-017-1492-y
    [4] A. Pratap, R. Raja, C. Sowmiya, et al. Robust generalized Mittag-Leffler synchronization of fractional order neural networks with discontinuous activation and impulses, Neural Networks, 103 (2018), 128-141. doi: 10.1016/j.neunet.2018.03.012
    [5] Q. Sun, M. Xiao, B-B. Tao, et al. Hopf bifurcation analysis in a fractional-order survival red blood cells model and PDα control, Adv Differ Equations, 10 (2018), 1-10.
    [6] J. Sabatier, F. Guillemard, L. Lavigne et al. Fractional models of lithium-ion batteries with application to state of charge and ageing estimation, Lecture Notes in Electrical Engineering, 430 (2018), 55-72.
    [7] K. Diethelm, D. Baleanu, E. Scalas, Fractional calculus: Models and numerical methods, Singapore: World Scientific, 2012.
    [8] M. A. E. Herzallahr, Notes on some fractional calculus operators and their properties, J. Fract. Calc. Appl., 5 (2014), 1-10.
    [9] J. Ma, P. Zhou, B. Ahmad et al. Chaos and multi-scroll attractors in RCL-shunted junction coupled Jerk circuit connected by memristor, PloS One, 13 (2018), 1-21.
    [10] S. Bhalekar, V. D. Gejji, D. Baleanu, et al. Transient chaos in fractional Bloch equations, Comput. Math. Appl., 64 (2012), 3367-3376. doi: 10.1016/j.camwa.2012.01.069
    [11] A. Razminia, D. Baleanu, Fractional synchronization of chaotic systems with different orders, P. Romanian Acad. A, 13 (2012), 314-321.
    [12] A. Jakubowska-Ciszek, J. Walczak, Analysis of the transient state in a parallel circuit of the class RLβCα, Appl. Math. Comput., 319 (2018), 287-300.
    [13] A. Buscarino, R. Caponetto, G. D. Pasquale, et al. Carbon black based capacitive fractional order element towards a new electronic device, AEU-Int. J. Electron C., 84 (2018), 307-312. doi: 10.1016/j.aeue.2017.12.018
    [14] P. Bertsias, C. Psychalinos, Differentiator based fractional-order high-pass filter designs, 7th International Conference on Modern Circuits and Systems Technologies, 7-9 May 2018, (2018), 1-4.
    [15] A. Obeidat, M. Gharibeh, et al. Fractional calculus and applied analysis, 14, Springer, 2011.
    [16] J. F. Gomez-Aguilar, J. J. Rosales-Garcia, J. J. Bernal-Alvarado, et al. Fractional mechanical oscillators, Rev. Mex. Fis., 58 (2012), 348-352.
    [17] F. Gomez, J. Rosales, M. Guia, RLC electrical circuits of non-integer orders, Cent. Eur. J. Phys., 11 (2013), 1361-1365.
    [18] C. Alexander, M. Sadiku, Fundamentals of electric circuits, 5 Eds., New York: Mc Graw Hill, 2013.
    [19] A. Tepljakov, E. Petlenkov, J. Belikov, et al. Fractional-order controller design and digital implementation using FOMCON toolbox for MATLAB, 2013 IEEE Conference on Computer Aided Control System Design, 28-30 Aug 2013, Hyderabad, India, (2013), 340-345.
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